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Search: id:A121585
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| A121585 |
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Triangle read by rows: T(n,k) is the number of deco polyominoes of height n and having k 1-cell columns starting at level 0 (0<=k<=n). A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column. |
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+0
2
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| 1, 0, 1, 1, 0, 1, 3, 1, 1, 1, 12, 5, 3, 3, 1, 60, 27, 14, 12, 6, 1, 360, 168, 83, 62, 36, 10, 1, 2520, 1200, 583, 393, 242, 86, 15, 1, 20160, 9720, 4698, 2941, 1845, 758, 176, 21, 1, 181440, 88200, 42606, 25285, 15856, 7151, 1990, 323, 28, 1, 1814400, 887040
(list; table; graph; listen)
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OFFSET
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0,7
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COMMENT
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Row sums are the factorials (A000142). T(n,0)=n!/2=A001710(n) for n>=2 Sum(k*T(n,k), k=0..n)=n!=A000142(n) for n>=1.
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REFERENCES
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E. Barcucci, A. Del Lungo, and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
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FORMULA
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The row generating polynomials satisfy P(n,t)=(n-1)!+(t+n-2)P(n-1,t) for n>=1 and P(0,t)=1.
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EXAMPLE
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T(2,0)=1, T(2,1)=0, T(2,2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 0 and 2 columns with exactly 1 cell starting at level 0.
Triangle starts:
1;
0,1;
1,0,1;
3,1,1,1;
12,5,3,3,1;
60,27,14,12,6,1;
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MAPLE
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P[0]:=1: for n from 1 to 10 do P[n]:=sort(expand((n-1)!+(t+n-2)*P[n-1])) od: for n from 0 to 10 do seq(coeff(P[n], t, j), j=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000142, A001710.
Adjacent sequences: A121582 A121583 A121584 this_sequence A121586 A121587 A121588
Sequence in context: A080214 A096066 A064085 this_sequence A010278 A137795 A070989
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 12 2006
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